5 Theories of Endogenous Growth

Economics 314 Coursebook, 2014

Jeffrey Parker

5 Theories of Endogenous Growth

Chapter 5 Contents

A. Topics and Tools ............................................................................. 1 B. What Is "Endogenous" Growth? ......................................................... 3 C. The Microeconomics of Innovation and Human Capital Investment ........... 6

Returns to research and development ..............................................................................6 Human capital vs. knowledge capital .............................................................................8 Returns to education.....................................................................................................9 D. Understanding Romer's Chapter 3 ...................................................... 11 Introduction ............................................................................................................... 11 The textbook's modeling strategy and the research literature ...........................................12 The basic setup of the R&D model ...............................................................................12 The knowledge production function..............................................................................13 Analysis of the model without capital ...........................................................................15 The R&D model with capital ......................................................................................18 Returns to scale and endogenous growth .......................................................................19 Scale effects in the R&D model ....................................................................................20 The (Paul) Romer model.............................................................................................22 E. Understanding Romer's Chapter 4 ..................................................... 22 The specification of the human-capital model................................................................22 Analysis with the human-capital model........................................................................22 Output per person vs. output per worker........................................................................23 F. Suggestions for Further Reading ........................................................ 27 General texts on modern growth theory.........................................................................27 Selected seminal papers in modern growth theory ..........................................................27 F. Works Cited in Text ........................................................................ 27

A. Topics and Tools

The neoclassical growth theory that we studied in Coursebook Chapters 3 and 4 largely evolved in the 1950s. There was considerable filling-in of details in the 1960s, but by the 1970s growth theory had largely become moribund. A tremendous revital-

ization has occurred since the 1980s, spurred by several shortcomings of the previous theories.

First, because growth rates are taken to be exogenous in the Solow and Ramsey models, these theories are unable to explain why growth rates (and, in particular, the rate of technological progress) might change from one time period to another. This became an important research topic in the 1980s when emerging data began to convince macroeconomists that productivity growth in the United States and other advanced countries had declined significantly beginning about 1974.

A second failing of neoclassical growth theory is that it cannot explain the large and lasting differentials in per-capita income that we observe across countries and regions. Solow's growth model implies more rapid convergence of incomes than seems actually to have occurred, particularly between developed and developing countries. International differences in technological capability can help explain this gap, but beg for an economic explanation that cannot be provided by models in which technology is exogenous.

Another feature of neoclassical growth models that some economists and policymakers find troublesome is that they provide no mechanism by which the saving and investment rate (or government policies directed at influencing it) can affect the steady-state growth rate. While this conclusion of neoclassical models is not obviously counterfactual, many find it counterintuitive and have explored models in which saving plays a more central role.

The pioneer of "endogenous growth theory" is Paul Romer, a former colleague but not a relative of our textbook author.1 His 1986 paper in the Journal of Political Economy is a seminal work in the modern revitalization of growth theory. The principal engine behind endogenous growth is the elimination of the assumption of decreasing returns to "capital."2 In order to justify this radical departure from a long-

1

In the early 1990s, there were three famous young Romers teaching macroeconomics at the University of California at Berkeley. Paul, who focuses on growth theory and is now at the Stanford Business School, David (our author), who is a prominent neo-Keynesian, and David's wife Christina, who is a macroeconomic historian and was chair of the Council of Economic Advisors in early years of the Obama Administration.

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This is a good time to clarify two closely related concepts: "diminishing marginal returns" and "decreasing returns to scale." The former is usually applied to changes in only a single factor of production holding all other factors constant. Thus, diminishing returns to capital means that when more capital is added to production with all other factors held constant, the ensuing increase in output becomes smaller as more and more capital is added. Returns to scale usually apply to the effect on output of simultaneous changes in many or all factors of production. "Constant returns to scale" by itself means that increases of an equal percentage in all factors leads to an increase of the same percentage in output. In this chapter, we will extend the idea of returns to scale to situations where a subset of factors changes.

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established assumption of microeconomic theory, Romer and his followers have broadened the definition of capital to include human capital and/or knowledge capital. As we shall see, once this broader view of capital is adopted it is no longer obvious that there are decreasing returns. This leads to radical changes in the conclusions that we derive from models that are otherwise similar to those of Solow and Ramsey.

There are two basic models developed in these chapters: the R&D model of Chapter 3 and the human-capital model of Chapter 4. We will give attention to both.

The mathematical tools used here are largely familiar ones. To keep the analysis simple, Romer mostly reverts to the simple Solow assumptions about saving (and other static resource allocation decisions). The original literature on these models bases decisions on utility and profit maximization, which is more satisfactory, but the dynamic properties of the model are similar with constant growth rates, so Chapters 3 and 4 will teach you the essential features of the model without all the complicated mathematics that we saw in Romer's Chapter 2.3

As in previous chapters, we will be searching for steady-state balanced growth paths. To find these, we will usually look for situations in which the growth rates of the key state variables are constant. In most of the models of these chapters, there will be two state variables, either physical capital and knowledge capital or physical capital and human capital. We will use a two-dimensional phase plane that looks on the surface like the one in the Ramsey model, but is fundamentally different because in these models both variables are state variables that cannot jump, whereas in the Ramsey model c was a control variable that could jump vertically to adjust to changes in economic conditions.

B. What Is "Endogenous" Growth?

In the Solow, Ramsey, and Diamond growth models that we have studied, the growth rate of natural GDP is n + g. Although we do not usually use that term, it would be appropriate to characterize these models as "exogenous-growth" models. All growth in GDP comes from our exogenous assumptions about growth in the labor force and in technological productivity. If we disable growth in the exogenous "inputs" to production by setting n = g = 0, then the economy doesn't grow--all growth is driven from outside the model. If the exogenous "drivers" stop pushing, the economy will stop growing. In contrast, an "endogenous-growth" model is one

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Barro and Sala-i-Martin (2004) is a more advanced textbook that looks at more sophisticated versions of these models. Acemoglu (2009) is a more recent, and more mathematical, treatment. For those interested in learning about them, Econ 454 develops the more complete models.

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that works like a perpetual-motion machine--once it gets started, it will keep going indefinitely unless something from outside slows it down or stops it.

Solow set out to determine whether the self-perpetuating cycle of output, saving, and investment could lead to endogenous growth. Under his assumptions it could not. In Figure 1, the cycle diminishes each time around the loop due to diminishing returns to capital. Each successive increase in the capital stock leads to a smaller increase in output than its predecessor, so the process converges and the growth cycle peters out. The economy converges to a steady state in which the only engine driving growth is the exogenous increases in technology and labor input.

Output

Saving

Capital Stock

Investment

Figure 1. Solow growth cycle

Endogenous-growth theories find ways to alter the assumption of diminishing returns in order to allow an ongoing, perpetuating cycle. For example, the first model we study in Romer's Chapter 3 changes how we think of technological progress. Instead of an exogenous factor determined outside the model, we now think of technological progress as the result of intentional, endogenous research and development investments. Just as investment in structures and equipment leads to increases in the capital stock (K), investment in R&D leads to increases in the stock of technical knowledge (A). Figure 2 shows the augmented growth cycle typical of an endogenous-growth model.

Unlike the Solow model, the cycle of Figure 2 need not diminish as it repeats. While physical capital surely has diminishing marginal returns with a fixed labor

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force and a fixed stock of technology, it is not obvious whether improvements in technology as a result of R&D will be subject to diminishing returns.

Output

Saving

Capital Stock

Capital Investment

Technology

R&D Investment

Figure 2. Endogenous growth cycle

Indeed, in the production function that we used in the growth models so far-- with Harrod-neutral technological progress--the collective marginal returns to investing in both physical and knowledge/technology capital are constant. If both K(t) and A(t) increase by 20%, we get a full 20% increase in output. If this leads to a 20% increase in investment in both physical and technology capital, then the cycle perpetuates undiminished.

This is the basic idea of endogenous growth. Even if there is no growth in the labor force or exogenous improvement in technology, the model can sustain ongoing growth at an undiminished rate.

These models often have equilibrium growth paths, but they do not imply the same kind of convergence behavior as the Solow model. In endogenous-growth models, just because the U.S. has higher current levels of capital per worker and percapita income than Mexico does not mean that Mexico must grow faster if both countries have the same parameters. Without diminishing returns there is no reason why investments in additional (physical and knowledge) capital in the U.S. will be less productive than those in Mexico, hence no reason that they U.S. cannot contin-

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ue to grow just as fast as Mexico and maintain its advantage. Thus, endogenousgrowth models can explain why gaps between richer countries and poorer ones sometimes might not close over time, even if the two countries have similar parameters.

C. The Microeconomics of Innovation and Human Capital Investment

Romer's Chapters 3 and 4 examine the macroeconomic implications of investment in research and development (innovation) and human capital. However, some of the most important theoretical issues in modeling these concepts are microeconomic in nature. The seminal papers in the modern growth literature vary a lot in how carefully they model these microeconomic issues, but Romer's simplified presentation of the models largely ignores the microeconomics. In this section, we briefly consider some of the basic microeconomic issues involved. (Romer discusses some of these topics in Section 3.4.)

The models of Chapter 3 attempt to make endogenous the "production" of technology. In the R&D model, an R&D sector produces additions to society's stock of technical knowledge. In Chapter 4, individuals add to their human capital by spending time in education rather than producing output.

A key microeconomic issue that underlies this analysis is the question of what incentive people have to make investments in knowledge or in human capital. Unless people get utility directly from the process of research or education (which cannot be ruled out--consider the case of the "professional student"), they will only undertake these investments if they are able to profit from them sufficiently to justify the opportunity cost. The opportunity cost of investing in research or education may include both forgone consumption and the lost alternative opportunity of investing in (and earning a return on) physical capital. Thus, if rational agents invest in research or education, then the earnings from these activities must have an expected present value at least as high as the current consumption that must be forgone and as high as the expected present value of the returns to physical capital investment.

Returns to research and development

As Romer discusses on page 117, pure knowledge is nonrival, meaning that the use of knowledge by one person does not reduce the ability of others to use it. Most "private" goods in the economy are, by contrast, rival. To clarify the distinction,

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think about chocolate-chip cookies.4 Everyone can use the same (non-rival) recipe for chocolate-chip cookies but everyone cannot use the same (rival) chocolate chips.

As you learned in Econ 201, a competitive market economy (in the absence of externalities) can lead to the production of the efficient amount of traditional, rival goods. The market price provides producers and consumers with a scarcity signal that can lead to efficient resource allocation by equating the marginal social cost of the good with its marginal social benefit. On the production side, producers equate price to the marginal production cost. Consumers consume at the level where the marginal benefit of an additional unit of the good equals the market price.

Nonrival goods such as knowledge can be reused by the same person or shared with additional people at zero marginal social cost. With marginal cost equal to zero, efficiency requires that people should consume knowledge at the level where its marginal social benefit is also zero. But, as with rival goods, utility-maximizing or profitmaximizing users of knowledge will "purchase" it up to the point its marginal benefit equals the price that is charged. They will choose the optimal level of use (where marginal benefit is zero) only if the price of knowledge is zero. Thus efficiency requires that knowledge, once it has been created, must be distributed freely at a zero price.

However, if the market price of knowledge is zero, then the market provides no financial reward for anyone who incurs the research-and-development costs that are necessary to create it. To provide such incentives, most countries have patent and copyright laws that grant exclusive (monopoly) intellectual-property rights to individuals who create knowledge. With a patent or copyright, the creator is able to charge a positive royalty for the license to use knowledge or to earn monopoly profits by using a newly discovered product or process exclusively and prohibiting its use by others. However, the argument of the preceding paragraph shows that charging a positive price for the use of a nonrival good such as knowledge leads to inefficiency, as does the existence of patent-protected monopolies. If individuals must pay to use knowledge, but the social cost of using it is zero, then they will choose to use knowledge at a lower-than-optimal level. Thus, when intellectual-property laws work as intended, they help resolve one problem by encouraging investment in knowledge, but at the same time they create another by discouraging its use. This argument is familiar to anyone who has followed the sometimes intense debates about illegal copying of software, works of entertainment such as CDs and DVDs, or about the pricing of pharmaceuticals.

In the chemicals industry, where the precise chemical formula for a molecule can be protected, patents usually provide excellent protection. However, in many other industries intellectual-property laws are less effective. For example, suppose that a

4

Some of us will use any excuse to justify thinking about chocolate-chip cookies.

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company discovers that a particular tool works better if it is curved than if it is straight. It can attempt to profit from its discovery by patenting the curved tool. However, there are many ways to curve a tool and it is probably impossible to gain patent rights on all possible curves that might be beneficially used. Once the knowledge that curved tools are better becomes public (as it does when a patent issues), everyone may be able to "invent around the patent"--adopt some variant of the improved technology without paying a royalty to the inventor. For such nonexcludable kinds of knowledge, inventors often resort to secrecy in hopes that it will be costly and time-consuming for competitors to discover or "reverse engineer" the knowledge. When knowledge is both nonrival and nonexcludable, it qualifies as a pure public good, with all the familiar resource-allocation problems that public goods entail. Governments often subsidize research and development for branches of knowledge where nonexcludability makes patent protection ineffective and where wide diffusion of the resulting knowledge seems especially important.

The issue of the efficient allocation of resources to research and development is a central focus of Reed's Economics 354: The Economics of Science and Technology. If you are interested in pursuing additional readings in this area, visit the instructor's Web page for a link to a recent reading list.

Human capital vs. knowledge capital

By human capital we mean acquired characteristics that make workers more productive. Although it encompasses such characteristics as health, strength, and stamina, the most commonly analyzed sources of human capital are the education, training, and experience that a worker embodies. Since education and training involve the transmission of knowledge, it might seem like human capital is the same as the knowledge capital we study in the R&D model.

However, there is a crucial difference. Knowledge capital is potentially a public good whereas human capital is not. An easy way of distinguishing between them is to think about the two major roles that most professors play. You see professors most often in the classroom, where they are imparting existing knowledge to students. This increases the students' human capital, but does not create new knowledge for society. When they are not in the classroom, your professors are likely to be engaged in research. If successful, this research leads to new knowledge capital that everyone can potentially share on a nonrival basis. Thus, simply put, society's knowledge capital is everything that is known by someone in the society; your human capital includes your personal familiarity with and ability to use part of that knowledge. Your human capital is personal to you--the fact that you have obtained knowledge may make you more productive but it does not usually raise anyone else's productivity. Thus human capital does not have the public-good characteristics of knowledge capital.

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